How do Archaeologists pay for their access to the literature they need to read now? And how much?
The reason why you are worried about pay to publish rather than pay to read is probably because you feel that reading is free or almost: your institution is paying for your reading, most probably.
Well, let’s transpose into the new paradigm: with the savings made by no longer having to pay to acquire publications, your institution will be able to pay for you to publish… Simple. As long as “pay to publish” does not become another rackett.

First, let me say that I believe that Open Access is the way forward. The current situation is not substantial and does not meet the needs of the majority of people.

I just do not think that this version of authors pays is the way forward, at least for archaeology. I will layout why here:

Archaeology deals with hard science money requirements on a humanities budget. Archaeology projects require a battery of tests from C14 dating (at least $250 per sample) to isotope analysis, all that cost a large amount of money. The total spending on archaeology by the National Science Foundation in the US is on the order of $5 million spread out among 400 departments in the US. There are at least 2000 archaeologists working in academia which roughly translates to $2500 per archaeologists, barely 10 C14 samples. The cost of one publication with author pays is roughly $750 about 1/3 of this amount. There is simply not enough external funding to support an authors pays model.

As for departments paying this is not viable either. The budgets are just too small to support a author pays. I’ll use my University, Edinburgh, as an example:

Assuming each staff member and researcher (22 roughly) on average publishes once a year and 1/3 of PhD students (30 students) publish once a year that would require a total of 16000 euro or $24000 a year.

I can say that Edinburgh does not, in its current publication budget, have the funding to cover that.

Author pays is not any more viable then the current set up BUT that is because profit is involved. PAGEPress is a for-profit company and so a large percentage of the costs is going towards making someone rich. Cutting out profits might lower prices into a range that is more viable for author pays. Though in its current state this version of author pays does not seem to be financially viable in the field of archaeology.